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## Posts

Teenagers With Attitude!

Fuck that noise.

I don't want to even try to think about g_64, just in case I accidentally manage to. Somebody finds me in my apartment days later. Brains, hair, and tiny little digits plastered to all the walls and ceiling.

il faut calculer pour vivre et non vivre pour calculeralso, my old phone number almost fits perfectly at a certain point in pi

Personally I'm not a fan of ONE specific mathematical discipline, but I like sequences and series

I'm pretty sure all phone numbers fit perfectly at some point in pi

in sequence?

6 numbers in a row is pretty cool

especially since they're pretty close to the decimal mark

i just finished my second engineering math.

fuck cycloidswell, close to the decimal is a different matter

but I mean you've got an infinite number of digits to work with back there if you count far enough, so every 6 digit sequence kind of has to appear somewhere

thirtyyears ago on a typewriter and always does the same exams, only with slightly different numbers.It's a joke really, and hadn't I taken some other math courses before I wouldn't learn a thing

But this way when a problem comes up, I just take one of my trusty books and learn it myself

from what i remember (Science, 2004ish so probably outdated), it's hardly random.

a few are statistically close, such as movement of alpha particles, i think.

Set theory is where I'm resting my head at the moment. All math is encompassed by set theory. Ofcourse, I've only got experience with undergrad math.

Don't worry, you can't. It's hopelessly huge. a googol you can actually write out. You can fit that shit on a piece of paper. g_64, no way. You can't even write out the number of digits in it. You can't write out the number of digits in the number of digits in g_64. You can't even write down the number of levels of digit-counting you would have to go through to get to something you could write down.

If you were to turn the entire universe into a computer capable of representing a digit with each individual particle, and were to crank the speed up so that you were refreshing every Planck time (the theoretical smallest possible interval at which time can be distinguished from space, something like 5*10^-44 seconds), over the entire lifetime of the universe, you wouldn't even have covered a perceptible fraction of g_64.

Here's the mind-fuck, though:

your = belonging to you

their = belonging to them

there = not here

they're = they are

Well, it goes further than that

everything is somewhere in pi

Think about it: Because it never repeats, and continues infinitely, it must at some point take every possible combination of numbers

which means everything,

everythingis represented somewhere in it's digits.Hamletin standard ASCII. The numbers one through four in such a sequence so that, if mapped to the letters TAGC, they would represent your genetic code. A jpeg of your face.A binary video file of your entire life, from birth to death.Now

that'sa mindfuck.INAPPROPRIATE APOSTROPHE

I hate being jailed :/

I'd argue it on the aesthetics. With 0! = 1 you get a nice, simple primitive recursive function, namely

f(0) = 1

f(n+1) = f(n) * n

If 0! were something other than 1, you'd define !n as f(n) everywhere except 0, where it would disagree. If your students argue about the natural numbers starting at 1, tell them about Peano's axioms.

I love math.

Sorry, pet peeve:

Pi is, in fact, sufficiently random that any string of digits appears within its decimal expansion with probability one. However, never repeating is not sufficient for this amount of randomness.

Consider: Let alpha be the sum of 10^-n! as n goes from 0 to infinity (for those who read TeX, /alpha = /Sum_{n=0}^{/infty} 10^{-n!}). It can be shown that alpha is not merely irrational, alpha is transcendental, (i.e. There's no polynomial with rational coefficients such that alpha is the root of that polynomial) however irrationality is enough for alpha to consist of an infinite string of digits that never repeats. But the only digits in the decimal expansion of alpha are 0 and 1. Thus, it cannot, e.g., contain your mom's phone number.

I'd just like to point out that it's not necessarily the case that a sequence that never repeats and continues infinitely will at some point contain every possible combination.

For instance, if you were to take the digits of pi pi and replace each 8 with a 4, you'd still have a non-repeating infinite sequence of digits, but it will never contain Jenny's phone number. Similarly, there are a lot of patterns that will never appear in 1.101001000100001000001000000100000001... even though it never repeats and continues infinitely.

Now, this does indeed seem to be the case with pi, and its digits do conform to roughly the same distribution as would be expected by random noise in the long term, but that's not a consequence of its infinite non-repetition.

Here's an interesting question to which I do not know the answer: is there a point in the decimal expansion of pi where it repeats everything that has gone before? I don't mean repeating in the standard sense, I mean, say it started 3.14159265358979

314159265358979323846, i.e. it repeats everything that has come before and then continues with other, non-repeated digits. It seems like this would have to happen, but I can't say with certainty.I would also asume that if this could occur at all, it would occur an infinite number of times.

your = belonging to you

their = belonging to them

there = not here

they're = they are

For a given digit index n, the probability that this digit ends a string of length n (ie, everything up to that digit) which is then repeated by the next n digits is 1/(10^n). The sum of this series as n goes to infinity is simply .1111..., or 1/9. In other words, the chance of there being any such sequence at all is 1/9; Thus I would conclude that there is almost surely not an infinite number of such sequences.

This of course assumes the digits of pi are randomly distributed; if somehow it turns out they're not then who knows.

The autistic savant who sees numbers as images in his mind amazes me

He can do these incredibly complex calculations simply by describing the picture he sees in his head

Also the dude recited pi to an obscene number of places

You mean the Rain Man guy?

Or the guy who isn't actually autistic but still has the mind like a savant?

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The scary part about him reciting pi is, he didn't memorize it or anything

No he just kept describing the picture in his head

The mind is a strange thing

It was previously thought inordinate strength in one area of the brain necessarily meant retardation in another

But that guy proved that wrong

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It's been so long since I've done anything math-related that I'll pretty much agree with anything that remotely makes sense, but that seems right (at least for the first occurrence, because once it happens and takes up a span of 2n digits, it's impossible for it to happen again until

at least4n; and even though pi is infinite I'm sure that still slightly affects the probability of it reoccuring...god, I hate statistics).But if pi truly is random and infinite and, for any sequence of infinitely large ns the probability of this occurring doesn't ever reach/approach 0 (and this is what I'm trying to think about now), then Fram's probably right and it would be expected to occur an infinite number of times, however infinitely spaced out the n-point of each occurrence would be from one another.

I think my brain just exploded.

Teenagers With Attitude!

The string

5318008occurs at position 13,809,596... so, clearly the universe got bored one day and decided to screw around with its calculator.Such as there is an infinite amount of numbers between 0 and 1. However, there are the

exactsame amount of infinite numbers between 0 and 2.The weird part is, if you take the amount of rational real numbers between 0 and 1 (1/2, 1/3, 1/4, 1/5, etc.), they are dwarfed by the amount of irrational real numbers between 0 and 1.

Or something like that.

I never really paid attention, I just seemed to recall the jist of it

Was that the guy who learned icelandic in like a week? That shit is just ridiculous.

kpop appreciation station i also like to tweet some

You should look into countable vs uncountable sets. The most common example is the rational vs irrational sets. It's pretty neat...I'd explain it, but I'm not Framling. I can't remember shit.

What I find more interesting is botched math proofs.

The Integers {...-3, -2, -1, 0, 1, 2, 3...} are a countable infinite set, because you can map them to the natural numbers; one such mapping can be achieved by mapping 0 to 0, positive numbers p to 2p and negative numbers n to -(2n - 1). So there are the same number of positive integers as there are positive and negative integers.

The set of real numbers between 0 and 1 is an uncountable infinite set. The easiest proof of this is by a simple contradiction: If every real number is accounted for, then there must be a real number whose first digit after the decimal is different than the real number mapped to 0, whose second digit after the decimal is different than the real number mapped to 1, whose third digit after the decimal is different than the real number mapped to 2, and so on for every decimal after the digit (the number of digits after the decimal in any real number is a countable set). The real number we just defined is not represented by a natural number since it's different from every real number that's being represented by a natural number, therefore it is impossible to map all decimal numbers between 0 and 1 to the set of natural numbers. So there are more real numbers between 0 and 1 than there are integers.

surprisingly, the newest number of all is seven hundred and twenty one, which, despite its rather innocuous standing in the grand scheme of things, was only introduced a couple of weeks ago

Botched math proofs are not new.

Transfinite numbers are not new.

Most of the shit in this thread is not new.

Except to the people in the thread who've never heard of them.

Which is kinda the point of the fucking thread.

So, who wants to hear about Turing's incompleteness theorem and Busy Beaver functions?

your = belonging to you

their = belonging to them

there = not here

they're = they are

imo

you'regayseems you and math just might hit it off after all